Ionic Hydration Radial Distribution Function;

Local changes of solubility induced by electrolytes: salting-out and ionic hydration

B.E. Conway

Chemistry Department, University of Ottawa, Ottawa KiN 9B4, Canada

Abstract -A comparativeexamination of electrostatic distribution treatments of salting-out and other approaches such as "scaled particle theory" is given. Treatments that take into account some ion-specific parameter such as the radius of the primary solvation co-sphere or some related equivalent quantity such as the ion's partial molal volume, give best agreement with experiment. Structural effects of a non—electrostatic kind are important in associated solvents but are most difficult to deal with in a satisfactory a priori way.

Analogiesare drawn between salting-out of non-electrolytes at ions and the surface-charge dependence of adsorption of neutral molecules in the double-layer at polarized electrode interfaces.

INTRODUCTION

PhenomenoloWand approaches The solubility of non-electrolyte solutes (1) in solvents (2) is usually specific to the molecularstructure, polarity and donicity of the 1 ,2 binary system, corresponding to the standardfree energy change, Lt°,ofthe solution process. Ifcomponent 1 is a dilute gas,solute-specific effects arising from intermolecular interactions in the solid or liquid lattices of 1 are avoided, making the interpretation of specific t°valuesfor 1,2 mixtures one stage less complex.

Since salting-out (or salting-in) effects are measured by changes of solubility, we are fortunately not concerned directly with the specificities that arise in solute solubility itself on account of solute size, polarity and polarizability, H—bonding etc., although these specificities have some indirect role in determining the changes of solubility inducedby ions through non-electrolyte and ion-solvation co-sphere interactions in near neighbor encounters.

In the presence of a dissolved dissociated electrolyte, a fraction of the solvent molecules, dependent on the concentration and stoichiometry of the dissolved salt, suffer solvational interaction with the ions and thus becomes diminished in activity, leading to "salting-out"of the dissolved non—electrolyte solute (2). The solvation of the ions of the electrolyte also leads to a self-salting-out effect which is a significant factor determining the activity behavior (Ref s. 2,3) of electrolytes at concentrations > ca. 1M.The formal thermodynamics of these situations is easily represented by the eqiiitions belowbut an a priori quantitative account of salting—out effects is quite difficult to achieve if saTt ion specificities aretobe at all well accounted for. Adequate theories of salting out must take into account: a) the structure of the solvent (Refs. 4,5) in the absence of solutes, and its own radial distribution function; b)changes of structure and entropy of the solvent (Ref. 6) in the neighborhood of cations and anions of the electrolyte and in the neighborhood of the non- electrolyte solute; c) the distribution functions for solvent around the ions and the non—electrolyte solute; d) the electric polarization and associated dipole orientation about the cations and anions of the electrolyte (usually ion- and charge-specific) and e) the average integrated effects associated with factors (a) to (d) about the ions out to several molecular diameters of solvent molecules from the ions.

263 264 B.ECONWAY

Calculations of salting—out effects thus involve most of the complexities of calculations of ion solvatlon (Ref. 7) wIth the added complication of the distribution of a polar, or non-polar, non-electrolyte near the ions in the region where the ions' strongest influences on the solvent structure and polarization normally arise.

Several types of calculation of salting-out effects have been performed or maybe envisaged: a) electrostatic distribution calculations for solvent and non-electrolyte solutes (Debyeand MacAulay (Ref. 8); Butler (Ref. 9); Belton (Ref. 10); Conway, Desnoyers and Smith (Ref. 11)); b) quasi—thermodynamic calculations (McDevit and Long (Ref. 12)), taking account of volumesof the species involved; c) scaled—particle theory (Ref. l3),based on empirical density information Refs. 14,15)); d) molecular dynamics calculations (e.g. of Heinzinger (Ref.16)) of the type applied to ion-solvent interaction, and distribution (not yet applied to salting-out, to our knowledge); e) dispersion and electrostatic energy calculations in distribution-type evaluationsof salting-out effects (Bockris, Bowler-Reed and Kitchener (Ref.17)).

Most work on salting-out has been done in highly associated solvent media -waterand alcohol/water mixtures (Ref. 17). In some ways, however, such solvents present the greatestdifficulties In developing quantitative, ion—specific accounts of salting—out owing to the role of structural changes (and associated entropy effects) Induced locally in the H-bonded solvents by the ions of the added electrolyte. Easier interpretationc mightbe achieved In work on unassociated but polar aprotic solvents such as CH3CN and DMSO. However, in such solvents, a complication of a different kind arises: In all but the most dilute solutions, electrolytes that are employed to study the salting effect remain substantially Ion-paired. Someadvantage arises In treating the salting—out of spherical or quasi-spherical non- electrolyte solutes, e.g. noble gases, CHk, C(CH3)L+ since the geometric distribution of solvent molecules around the solute is spherical and no localized dipole, asymmetrically situated in the molecule, is present.

TREATMENTS OF SALT EFFECT ON NON-ELECTROLYTE SOLUBILITIES

1. Formalthermodynamics. Saturation solubility equilibrium of a substance between e.g. thegas-phase, g, and a solution phase, s, is determined by the condition = i.e.

t°g+RT in fg= °5+RT in S° +RT in -y° (1) where f is the fugacity of the gas, S° the saturation solubility in pure solvent and y the act?vlty coefficient,usually taken as 1 inthe pure solvent. In the presence of a salt,S°Is changed to S and y° to y, due mainly to the Interaction of the salt ions with the solvent. Then in S0/S =iny. (2)

Salting-out arises when y> 1 and salting-in when y <1. Usually the change of in y is linear with salt concentration, c, In dilute solutions so that in S°/S =kc (Setschenow's relation). From eqñ. (2), It is clear that calculations of the solubility ratio or of Setschenow's constant krequire evaluation of the non-ideal free energy of non-electrolytesolute caused by the presence of ions. By notIng that 50_5= S,the change of solubility, an alternative relation

LS/S°= kc÷ (3) arises fromSetschenow'sequation for sparingly soluble solutes.

2. ElectrostatIctheories. Early electrostatic theories were based on the followIng approaches:

a) calculation of RT in y Is made (Debye and MacAulay (Ref. 8)) In terms of the differenceof charging energy of the ions ofthe electrolyte in the pure solvent and in the non-electrolyte-containing solutionbroughtabout by the fact that the non-electrolyte, i •usuallychanges the dielectric constant of the solvent. RTlnyis then obtained intermsofthedielectric decrement Sofiin the solvent. For mostnon-electrolyte solutionsin water,this treatment predicts salting-out. In a number of cases, these predictions for various salts are neither Salting-out and ionic hydration 265

quantitatively nor qualitatively in agreement with experiment. This treatment has all the well—known (Ref. 11) deficiencies associated with use of the Born equation in a very polar medium such as water. b) AS/S° (eqn. 3) is calculated by means of a treatment in which the distribution of solute i in comparison with that of solvent molecules is evaluated around the ions of the electrolyte. A Boltzmann relation is generated in terms of the differenceAU of electrostatic polarization energy suffered by the "gas' molecule in te field of an ion in comparison with that of an equal volume of solvent at thesame distance r from the ion. Integrationof this effect from theradius of the ion a to infinity [or f9.,aco-sphere radius R, dependent on ionicconcentration cT1R= 3000/4ILNAc÷)"),givesthe relative solubility change AS/S°. This was the basis of Btitler s method (Ref. 9), as also employed by Bockris and Egan (Ref. 17), and Bockris, Bowler—Reed and Kitchener (Ref. 17).

These treatments suffer from three serious weaknesses: (i) the Boltzmann factor in the polarization energy difference AUe/kT was linearized which, near the ion, where the field is high, is inadmissable; (ii) dielectric saturation effects, important near the ion, were not considered (this factor makes it more inadmissible to linearize the Boltzmann exponent); (iii)theterm used (Refs. 9,17)for electrostatic polarization of the solvent was inappropriate for an associated liquid such as water where dipole reaction—field and correlation effects in the polarization have to be considered (Belton (Ref. 10) recognizedsome, but not all, of the latter difficulties). However, Bockris, Bowler-Reed and Kitchener (Ref. 17) introduced a quantitative treatment of dispersion interactions intosalting-out theory which is important in salting effects between relatively large polarizable solutes and large ions, e.g. of the RLIN+ type, where salting-in may arise. Conway, Desnoyers and Smith (Ref. 11) improved the distribution-type theories by taking account of the dielectric saturation effects and avoiding linearization of the Boltzmann factor by performing the required integration (Refs. 9,10,11) over twointegrands:one, nearthe ion (Fig. 1) where Ue/kT>> 1 and dielectric saturation is important, and the other further from the ion, beyond the primary hydration shell of radius rh, (Fig. 1), where linearization is permissible. Fortunately, near the ion, the dielectric saturation effects do not have to be numerically evaluated since they appear in Ue for conditions whereUe/kT>>l,so that exp[-Ue/kT] ÷0.

I I 'I / N /

'a—' r

Fig. 1 Schematic diagram ofregion of polarization influence about two ions showing the cosphere radii rh and R. 266 B. E. CONWAY

Their equation for tS/S° was (Ref. 11) R 4A 2 k =tS/S°c± = (1—exp[..tUe/kT])r d: •Tö•ö (4) a

h 4N 2 4iINA I AU 2 = [Ue/kT])r dr + r dr :i-o. .. (1-exp (5) 'h Theelectrostatic energy iUe was taken as

tUe (E2/8itNA)(V60 —9P/2) (6) whereP is the polarization of non-electrolyte given by 4. ILNA(a+i/3kT), V is the partial molar volume of non-electrolyte, c the dielectric constant of the solvent and a thepolarizability of i. =l/9(n2+2)22where n is the refractive index and thedipole moment of the non-electrolyte. (cE2/8iN,) V corresponds to the polarization energy which solvent molecules experience in the field E of the ion. The first integral ineqn. (5) can easily be evaluated when AUe/kT >>1,as it normally is near the ion (a

Introduction of this parameter rh allows specificity of ion-solvent interaction to be taken into account since rh measures an effective radius of the primary solvation shell (Ref. 19) within which the ion-solvent interaction energy is usually >>kTand dielectric saturation obtains. Within this region, no errors of linearization of the exp function arise.

Afurther improvement (Ref. 20) to this type of theory is the introduction of the radial distribution function g÷ 5(r) of the solvent, s, about the ions, ±,sincethe integration should not be performed'especially near the ion, as though the solvent were a continuum. g÷ (r) allows some account to be taken of the discontinuous nature of the solvent near tM ions. In practice, however, few dataare yet available for g functions except for a few salts studied by Narten (Ref. 5). Introduction of g÷ tAnsforms eqn. (5) into -,

As/s°c =4N [h r2g 5(r)dr +$ (E2/8kTN)eg±(r)r2drJ(E2/8kTNA) p r2 dr] (7) g5(r) does not enter into the last integral since that term involves interaction between nbñ-electrolyte (n.e.) and the ions and nothing is known about gne s(r) for non-electrolytes, althoughit is important for refinement of calculations invoTving ion non-electrolyte co-sphere encounters. As in eqn. (5), the first integral in eqn. (7) deals with the almost complete exclusion of i from the primary solvation shell of the ion. In practice, eqns. (5) or (7) must be written (for a simple 1:1 electrolyte) as the sum of two sets of terms, one for the cation and one for the anion, each with its respective ionic parameters (a, rh).

While electrostatic calculations of sal ting-out of gases give a fair account of the trend of AS/S° with ionic charge and radius for a given gas salted-out by a series of salts, they donot give any basis for specific solute and solvent structure effects in salting-out. Such effects are very difficult to calculate from first principles and would require de- tailed knowledge of the radial distribution functions g+,(r), g_ ne(r) and g, 5(r), and of any dependence of gne 5(r) on the presence of the ion for situations where n.. is near an ion (co-sphere interaction effects).

3. Non-electrostatic factors. Usually, dissolution of a solute is accompanied by an enthalpychange and for a series of solutes in a given solvent or for a given solute in a series of solvents, the AH° and AS° changes compensate each other to give a standardfree energychange for the dissolution process that is relatively less sensitive to the nature of the solute or solvent. This "compensation effect" is especially significant for water where heat changes associated with H-bond breakingor making are accompanied by respective positiveor negative entropy changes. Specificities in salt effects on gas solubility can arise because of changes in either or both the iH° or the TAS° components of the free energyof solution of the gas, due to local changes of H bonding in the water, brought about by the ion-water interaction. Salting-outandionichydration 267

Dissolution of a gas atom or molecule requires first the formation of a cavity (Ref. 21) ofsuitable size in the solvent. The cavity formation process itself involves an entropy and enthalpy change. After the gas particle has entered the cavity, new interactions betweenthe solvent particles and the solute arise with a corresponding entropy change. Restrictionof the particle to a "free volume box" in the solvent usually involves a substantial loss of translational entropy while the reaction of the solvent particles surrounding the solute may involve an increase or decrease of entropy, especially in water, depending on whether hydrophilic or hydrophobic interactions predominate.

Inthe case of a polyatomic gas, dissolution will also result in loss of some rotational entropy as the particle suffers restrictions to its rotational freedom (libration). The partition function for libration is

=8i2(8,t3I1I2I3k3T3)1"2 sinh IJL/kT h3 U/kT i.e., the rotational partition quotient, which is the term before the sinh, is multiplied by the function sinh UL/kT /UL/kTwhere UL is the potential well in which restricted rotational oscillations arise. It is obvious that as UL/kT ÷0,q + andthe entropy increases; conversely, when UL/kT >>1,the entropy is decreased.

In the case of polyatomic gases, the entropy associated with restricted rotation will itself be sensitive to solvent-structure around the cavity in which the librations are executed, since UL will depend on how the H—bonding amongst water molecules in the cavity is affected by the gas particles occupying the cavity.

General factors in salting-out are listed in Table 1.

TABLE 1. Factors in saltinq—out

A) Energyfactors (i) Difference of electrostatic polarization energy of non-electrolyte solute and an equal volumeof solvent, by the ionic field. (ii)Van der Waals dispersion forces [significant for large non-electrolytes and large ions (giving salting-in tendency; cf. Ref. 17)].

B) Structural energy and entropy factors

(i) Modification of radial distribution function for solvent by (a) ions and (b) gas solute.

(ii) Modification of cavityformation energy for cavities formed near ions. (iii)Modificationof cavity reaction behavior when gas enters cavity near an ion in comparisonwith cavity in free bulk solvent.

(iv) Hydrophobic bonding with certain ions by sharing of structure-enhanced regions aroundionand gas solute (co—sphere and cavity sharing).

(v) Dependence of librational entropy of polyatomic gases on cavity properties near an ion.

4. Treatments based on scaled-particle theory. In recent years, applications of scaled- particle theory (Ref. 13) to calculation of salting-out effects (Refs. 14,15) and related mattershave been made. The approach is based on Pierotti's (Ref. 13) use of the scaled- particle theory of Reiss et al. (Ref. 13) to calculate gas solubilities. Shoor and Gubbins(Ref. 15) applied this method to calculation of solubilities of He, H2, Ar, 02. CH4, SF6 and C(CH3)4 in concentrated aq. K0H (10-50 wt % - an unfortunate choice of conditions for testing of any theory related to electrolyte solution behavior),. Masterton and Lee (Ref. 14) extended Shoor and Gubbins' treatment to calculation of the salting effects for any salt/non-electrolyte pair. The solubility S in the salt solution is evaluated by regarding the electrolyte solution as a different type of "solvent" for the non-electrolyte from that in the absence of salt. 268 B. E. CONWAY

Thefollowing relation for S is obtained (Refs. 14,15)

(9) wheregis the free-energy of cavity formation, g ne the free-energy of introduction of non-electrolyteinto the cavity (this includes the energy of interaction with molecules in the walls of the cavity, plus any energy associated with Isreaction of thecavity [changes of H bonding and orientation] to the presence of the non—electrolyte). p . are numberdensities (particles per cc) of the various species 3in solution taken as - empiricalparameters in the scaled-.particle theory. The use of these empirical p3. it is to be noted, introduces an unfortunate empirical aspect into the treatment since specificitiesof ion—solvent polarizationand interaction are hidden in these terms.

Evaluation of the Setschenow coefficient k (eqn. 3) requires evaluation of the derivatives of gc gc ne and ln p3 with respect to ionic concentration. The last factor is relatively easily evaluated and gives a contributionto the overall salting—out coefficientof - =0.016-4.34x l0 V0 ( (10) k() = k3[see belc*i]) whereV0 is the partial molar volume of salt at infinite dilution and thus contains most of the factors of interest with regard to ion-solvent polarization interactions and electrostriction (cf. the treatment of McDevit and Long (Ref. 12). The contributions to k from dg/dc+ and dg ne'cc÷ are more difficult to calculate but the results, after some extensive ñiathematis, arê (Ref. 14)

RI=- 9,2°,2 + (11) [c1,3c,3 + Cl,4c5,4] [l 1X wherepis the dipole moment and a the polarizability of water, oj are intermolecular distances between 1 = 2 = 3 = non—electrolyte, water, cation and 4 = anion. e,q arecorresponding pair interaction potentials in the mixture, taken as cq (ccj)tçs while =(o,+ o)/2. Eqn. (11), it is seen, involves again V, which characterizes the ion-solvent interaction in this theory. And = g/kT —ln(l—-3)+ A (12) where 1 Ii+.i!L+32°l I (13) l—-3 L 2 2(l—T3)] The terms l' 2 and involve V, the radii of the species in solution, the ionic concentrations, and the density and molecular weight of the solvent. An expression can be deriyed for dgc/dc which involves only a series of numerical factors, the diameters a and the V°for the ionc components. The quantities required for the calculation of the overall kare, in summary, V° for the salt, the diameters and polarizabilities of the cation and anion, the diameter of non-electrolyte solute, the energy parameter e1/k and the polarizability a1 of the non-electrolyte.

Therelative val ues of the three sal ting-out coefficient contributions dg/dc ( = k), dg/dc± ( = k2) and d logp3 (= k3) are quoted(Ref. 14) for several systems:

System k1 k2 k3 Overall k (eqn. 3) H2/NaCl 0.126 -0.023 0.008 0.111 0.115 -0.031 H21"KI -0.004 0.080 0.203 -0.080 0.008 CH4/NaC1 0.131 0.182 -0.102 -0.004 CH4/KI 0.076 0.387 -0.194 0.009 0.202 SF6/NaCl 0.343 -0.226 -0.004 0.113 SF6/KI

For all systems k1 is positive which implies that it is more difficult to form a cavity in the ionic solution than in water itself. This is understandable, since the attractive interactionbetween an ion and solvent dipoles will make it more difficult to form cavities near the ions, i.e., where the salting-out effects originate. Salting-outandionidhydration 269

Thenegative values of k2 are interpreted (Ref. 14) in terms of the non—electrolyte expe- riencing a net attractive force in the cavity when water molecules in the surrounding walls of a cavity are replaced (in part) by an ion. This is expected, since the non- electrolyteexperiences polarization interactions due to the field E of the ion (—1/2 1 Er). This effect Is thus analogous to pj of the dielectric polarization energy iference term tU employed in the distributThWtype theories. The k3 terms are relativelysmall. The other part is involved in the energy required to form a cavity nearan ion, a process in which water molecules must be removed from their favorable position of interaction with the ion. It is evident that this part corresponds to the ion-solventdielectric polarization component of the 1e term of eqn. (4). The advantage of the distribution type theories is that these energies are calculated directly and their difference determines the salting-out coefficient after integration over the volume ofsolvent Influenced by the ions. Specificities in ion—solvent interaction which are reflected in the experimental dependence of k on the identity and charge-type of thesalt are included in the scaled-particle treatment in the V and terms.

It has been stated (Ref. 15) that an advantage of the scaled—particle theory is that all structural aspects of the Interaction of the solute with the solvent (cf. Ref. 6) are eliminated. The method therefore obscures the electrostatic Ion/solvent and Ion/solute interactions that are of essential interest in salting—out and are predominant and often specific for small ions. Structural and electrostatic properties of the solvent or solutionare contained in the number densities for components of the solution (which are requiredas empirical data) and in g which Is mainly entropic (Ref. 20) In the aqueous medium case.

In the application of this theory to salting-out phenomena, it is claimed (seemingly as an advantage) that the treatment "makes no appeal to assumptions concerning solvent structure, ionic hydration, etc.. and that, in addition, "the ionic charge has little direct influence on salting_outis. It must be stressed, however, that there is clearly demonstrable experimental dependence of salting-out constants (Refs. 11,12), k, on ionic charge and radii in salt solutions, but that the effects are obscured by use of empirical densities in the scaled-particle theory; the essential electrostatic effects (primary hydration,solute and solvent polarization, etc. )arecontained in the densities or V dataintroduced empirically, as they are in McDevit and Longss theory (Ref. 12).

In fact, the salting-out is really evaluated as the difference of solubility in two kinds ofsolvents, the ion—free and the ion-containing one without any direct reference to the essential electrostatic interactions and structural modifications which ions are known to make in polar solvents, especially water.

Statistical-mechanicaltreatments of salting-out effects have been given by Haugen and Friedman (Ref. 22) and by Krishnan and Friedman (Ref. 23). In the former paper, simplifications were introduced which made the treatment equivalent to earlier electrostatic calculations. In the latter paper, Setschenow coefficients were calculated on the basis of a model, similar to that used in previous Ion-ion and ion—solvent interaction calculations, for which the interaction potential U as a function of distance r is given by

U.. =COR..(r) + er + (r) + (r) (14) e,e3/ CAV,LJ GUR,LJ TheCOR term is a core repulsion term, the CAV accounts for dielectric effects and the GUR termis a solvation-shell co-sphere overlap effect characterized by a parameter A,q having the significance of a free energy change per mole of solvent displaced from the co-sphereof and 3 due to their overlap. Unfortunately, one of the main ion—specific factors in salting-out,viz., the GUR term, was adjusted to fitthe experimental databy matchingexperimental k values by empirical introduction ofthe A,. values in GUR,3(r) forcation and anion. It seems that much of the elegance of the mthod of Friedman et al. is negated by the empirical assignment of the GUR,(r) term which expresses the main interaction causing salting-out (L= non—electrolyte,3 =cationor anion). In discuss- ing the case of benzene-ion interactions, Krishnan and Friedman (Ref. 23) conclude that the main defect In their model Is the omission of dispersion and charge polarization interactions. To us, these seem to be the main electrostatic interactions of interest in salting-out.

5. HydrophobIc co—sphere interactions leading to salting—in contributions

(i) Structure-promotion and co-sphere sharin

Salting-in arises with a number of systems for which simple electrostatic theory (Refs. 8,9,11) would predict salting-out. Bockris et al. (Ref. 17) showed how introduction of dispersion interactions could account for such effects. However, calculation of their dielectricpolarization contribution was based on over-sim- plifieddielectric theory for water. Desnoyers et al. (Ref. 24) showed how sharing of co-spheres of an hydrophobicnon-electrolyte (benzene) and an 270 B. E. CONWAY hydrophobic ion (R4N type) could lead to salting-in effects without recourse to calculation of dispersion interactions (although tTise will always be significant [cf. 17,20]for large ions). A statistical mechanical approach to calculation of such effects with neutral molecules was given by Ben-Naim (Ref. 25) on the basis of free energies of solution of "monomer" and equivalent "dimer" species, associated on account of "hydrophobic bonding". The case of CH4 and C2H6 ("dimer of methane") was considered; the freeenergy of hydrophobic association was expressed as the difference of the standard freeenergies of solution, L°CH6- 24CR4'ofethane and methane. The anomalous nature of water as a medium 1eaing to hydrophobic bonding is closely connected with its anomalous behavior for dissolution of such solutes at infinite dilution where unusual entropies and heatcapacities of solution comonly arise.

Despite the elegantstatistical mechanical presentation of the hydrophobic interaction effect by Ben-Naim,its evaluation is refer1ed to relatively simple empirical quantities such as 'C H and 26 CH (ii) An equally interesting approach can be made in terms of surface tension and cavity area, where co—sphere sharing leads to a diminution of local solute/water interfacearea and a net attractive interaction. 6. Comparative summary of theories of salting—out. Theories of salting-out and salting- inare summarized comparatively in Table 2 below:

TABLE2. Comparison of theories of saltlng..out andsalting—in - Theory Coments Authors/Ref. a) Born polarizationenergy Has weaknesses of Born polariza- Debye and MacAulay8 treatment tiontype of calculation (prob- lems of continuum dielectric, dielectric saturation, ionic radii, etc.) b) Distribution treatments (i) Butler Oversimplified dielectric polar- Butler9; Bockris ization calculation. Unjustified and Egan'7 linearization of exponentials.

(ii) Belton Improved treatment of non- Belton10 electrolyte distribution; more realistic polarization terms suggested.

(iii)Bockris, Bowler-Reed As in b(i), but inclusion of Bockris, Bowler-Reed andKitchener dispersion interactions gives andKitchener17 prediction of salting-in.

(iv)Conway, Desnoyers and Linearizationproblem and dielec- Conway, Desnoyers Smith; Conway, Novak tric saturation taken into account.and Smith11; and Laliberté; Specialrole of primary hydration Conway, Novak and Desnoyers and Arel shellincluded and solvent—struc- Lali berté20; ture entropy effects recognized. Desnoyers and Arel2 c) Scaled—particle theory Givesgood account of salting—out Shoor and Gubbins'5; treatments behavior and specificity for Mastertonand Lee various salts. Ion/solvent/non- electrolyte electricp01 an zati on effectsobscured by use of empirical density factors. Includes cavity effects. d) Thermodynamic compression Gives good account of salting—out/McDevit and Long12 (electrostriction) treatment in but is based on empirical electrostriction term which includes specificities in ion— solvent interaction. Salting-out and ionic hydration 271

TABLE2. Comparison of theories of salting—out and salting-in (cont'd)

Theory Comments Authors/Ref.

e) Statistical-mechanical Very sound in principle, but HaugenandFriedman22; treatments weakened by necessity for exten- KrishnanandFriedman23; sive simplifications and intro- Hall26 duction of empirical factors if numerical evaluations are to be made, e.g., use of empirical Gurney term.

7. Salting-out in relation to field effects on adsorption at charged interfaces: The problem of calculation of salting-out of non-electrolytes near ions is closely related to that of evaluation of potential or surface-charge dependence of adsorption of neutral molecules in the double-layer at electrified interfaces. The field due to ions is replacedby a double-layer field determined by the surface charge density on the electrode (or colloid) surface. Primary hydration has its analogue in solvent orientation in the double-layer in response to the field established by the charged surface.

The adsorption of a non-electrolyte is normally a maximum at or near the potential of zerocharge. Increasingcauses polarization of both solvent and non-electrolyte. The non-electrolyte is relatively excluded ("salting-out" field effect) from the compact region of the double-layer in relation to the solvent when the latter is more polarizable,per unit volume, than the adsorbate. Even for highly polar adsorbates, such as glycine (dipole moment, ca. 15D), adsorption from water at the Hg electrode is decreased by increasing electrode EFarge density.

The adsorption problem can be treated in terms of classical dielectric theory with an appropriatepolarization energy term for associated polar dielectrics. Alternatively, in recent treatments, the change of energy of adsorption with increasingcan be evaluated by calculating the energy required for displacing oriented solvent molecules in the double-layer by the non-electrolyte adsorbate. The energy of the solvent molecules increases with surface charge as also does their relative orientation. A two-state model with or + orientation was used. An adsorption maximum at = 0 is predicted with an almost correct diminishing extent of adsorption, analogous to salting-out, with increasing ± .

REFERENCES

1. V. Gutmann, Chemistryin Britain 7 (3),102—107 (1971). 2. G. Scatcharcf Phys. Zeit. 33, 32—1 (1932). 3.J.E. Desnoyers and B.E. Co7ay, J.Phys. Chem. 68, 2305—2311 (1964). 4.J.D. Bernal and R.H. Fowler, J. Chem. Phys. 1, T5—548 (1933). 5. A.H. Narten, J. Phys. Chem.74, 765—768 (1970T; J. Chem. Phys. 51, 1108—1114 (1969). 6. H.S. Frank and M.G. Evans, J. Chem. Phys. 13, 507-532 (1945). 7. B.E. Conway, Ionic Hydration in Chemistry iid Biophysics, Elsevier Publ. Co., Amsterdam (1982). 8. P. Debye and J. MacAulay, Z. phys. Chem. 26, 22—35 (1925). 9.J.A.V. Butler, J. Phys. Chem. 33,l0l5—102 (1929). 10. J.W. Belton, Trans. Faraday SoE7 33,653—659 (1937). 11.B.E. Conway, J.E. Desnoyers and Ai. Smith, Phil. Trans. Roy. Soc. London A256,— 389- 437 (1964). 12.W.F. McDevit and F.A. Long, Chem. Rev. 51, 119—169 (1952). 13. H. Reiss, H.L. Frisch and J.L. Lebowitz7J. Chem. Phys. 31, 369—380 (1959); 33, 1379— 1385 (1960); see also R.A. Pierotti, J. Phys. Chem. 67, T40-l845 (1968); 69728l- 288(1965). 14.W.L. Masterton and T.P. Lee, J. Phys. Chem. 74, 1776—1782 (1970). 15. S.K. Schoor and K.E. Gubbins, J. Phys. C!iem.73, 498—505 (1969). 16. K. Heinzinger and P.C. Vogel, Zeit. NaturforsEFi. —29a, 1169—1179 (1974); (1974); 30a,— 789-797 (1975); 31a, 476—483 (1976). 17.J. O'M. Bockris,J7 Bowler-Reed and J.A. Kitchener, Trans. Faraday Soc. 47,— 184-192 (1951); 18.J.T. Randall and C.F. Faley, Chem. Rev. 4, 271—318 (1927). 272 B. E. CONWAY

19.J.O'M. Bockris, Quarterly Rev. Chem. Soc. London 3. 173—180(1949);B.E. Conway and J.O'M. Bockris, Modern Aspects of Electrochemistry, Vol. 1, Butterworths, London (1954). 20. B.E. Conway, D.M. Novak and L. Laliberté, J. Solution Chem. 3, 683-711 (1974. 21. D.D. Eley, Trans. Faraday Soc. 35, 1281—1293; 1421-1432 (1939)7 22. G.R. Haugen and iLL. Friedman, TPhys.Chem. 67, 1757—1761 (1963). 23. C.V. Krishnan and H.L. Friedman, J. Solution CEIm. 3, 727-744 (1974). 24. J.E. Desnoyers and M. Arel, Can. J. Chem. 45, 359-3'6 (1967); ibid, 43,— 3232-3237 (1965). 25.A. BenNaim, J. Chem. Phys. 54, 1387 (1971); J. Phys. Chem. 77, 95—102 (1973). 26. D.G. Hall, Trans. Faraday SE. 67, 2516—2524 (1971).